A random fiber bundle with many discontinuities in the threshold distribution

TL;DR

This paper investigates a random fiber bundle model with multiple discontinuities in the threshold distribution, revealing universal critical exponents and non-universal avalanche behaviors depending on the distribution parameters.

Contribution

It introduces a generalized fiber bundle model with multiple threshold discontinuities and analyzes its critical behavior and avalanche distribution properties.

Findings

Critical exponents are universal across different threshold distributions.

Avalanche size distribution shows non-power law behavior for small sizes.

Behavior with multiple discontinuities is similar to the single discontinuity case.

Abstract

We study the breakdown of a random fiber bundle model (RFBM) with $n$-discontinuities in the threshold distribution using the global load sharing scheme. In other words, $n+1$ different classes of fibers identified on the basis of their threshold strengths are mixed such that the strengths of the fibers in the $i-th$ class are uniformly distributed between the values $\sigma_{2i-2}$ and $\sigma_{2i-1}$ where $1 \leq i \leq n+1$. Moreover, there is a gap in the threshold distribution between $i-th$ and $i+1-th$ class. We show that although the critical stress depends on the parameter values of the system, the critical exponents are identical to that obtained in the recursive dynamics of a RFBM with a uniform distribution and global load sharing. The avalanche size distribution (ASD), on the other hand, shows a non-universal, non-power law behavior for smaller values of avalanche sizes which becomes prominent only when a critical distribution is approached. We establish that the behavior of the avalanche size distribution for an arbitrary $n$ is qualitatively similar to a RFBM with a single discontinuity in the threshold distribution ($n=1$), especially when the density and the range of threshold values of fibers belonging to strongest ($n+1$)-th class is kept identical in all the cases.